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Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

$\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}$

when t = 1 hour, y = 15 grams. So,

$y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}$ (1)

when t = 3 hours, y = 30 grams. So,

$y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}$ (2)

dividing (2) by (1), we have

$\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}$

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

$A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36$

Substituting A and k into y, we have

$y = 18.36te^{-0.203t}$

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

$y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g$

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0

3 years ago

Increasing on the intervals<br><br> Decreasing on the intervals

tatyana61 [14]

The increasing and decreasing intervals are marked on the graph and attached below.

The red arrow mark shows the part where graph is decreasing

The green arrow mark shows the part where graph is increasing

There is no end point or starting point for the graph

The graph starts decreasing at -∞ and it decreases till it reaches -2.5

Also the graph start decreasing at 0 and goes to +∞

So we have two decreasing intervals

(-∞ , -2.5) U (0, ∞)

The graph starts increasing at -2.5 and it increases till it reaches 0

So increasing interval is

(-2.5, 0)

6 0

3 years ago

2. A line contains the points

V125BC [204]

Answer:

B

Step-by-step explanation:

equation of a line is in the form of y=mx+b where m is the slope and b is the y intercept

slope: -1-2/0-4 = 3/4

y intercept is when x is 0, so y intercept is -1

therefore the equation of this line is y=3/4x-1

4 0

2 years ago

24 is 16% of what number Explain how you got your answer)

Lemur [1.5K]

My teacher always taught me to set these problems up like a proportion

is / of = % / 100

24/ x = 16 / 100

16x = 2,400

Divide 2,400 by 16 and you get 150.

150 is the correct answer.

6 0

3 years ago

I need help can somebody help me pls asap

Phoenix [80]

Answer:

Yes, i can help the answer is d.

Step-by-step explanation:

The pie chart shows the data of each amount and d. is the answer that will fill and divide by 2 with no remainder

6 0

3 years ago

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